1. 5.3 Inequalities in One Triangle
Objectives:
Recognize and apply properties of inequalities to the measures of the angles of a triangle.
Recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle.

2. Concept

3. Example 1

4. Example 2

5. Practice #1 A. B. C. D. A. B. C. D.

6. Practice #2 A. B. C. D. A. B. C. D.

7. 65˚ 7 5
80˚
35˚ 8
20˚
75˚
85˚

8. Concept
5.5

9. Example 3 B 5 7 A C 9 What is the largest angle of the given triangle?
5.5

10. List the angles of ΔTVX in order from smallest to largest.
Practice #3
List the angles of ΔTVX in order from smallest to largest.
A. X, T, V
B. X, V, T
C. V, T, X
D. T, V, X

11. Practice #4 D E F 110° 46° List the sides from largest to smallest.
A. DE, EF, DF
B. EF, DE, DF
C. DE, DF, EF
D. DF, DE, EF
5.5

12. Practice #5
A triangle is formed by three kitchen appliances as shown in the figure. The distances shown are measured in feet. What is wrong with the labels?
5.5

13. 5.6 Inequalities in Two Triangles
Objectives:
Apply the Hinge Theorem or its converse to make comparisons in two triangles.
Prove triangle relationships using the Hinge Theorem or its converse.

14. Think about this…

15. Concept

16. Complete the inequality (or equation):
Example 4
Complete the inequality (or equation):

17. Complete the equation or inequality:
Example 4
Complete the equation or inequality:
3) m<1 ___ m<2 4) MS ____ LS 5) m<1 ____ m<2

18. Practice #6 A. Compare the lengths of FG and GH. A. FG > GH
B. FG < GH
C. FG = GH
D. not enough information

19. Practice #7 B. Compare mJKM and mKML. A. mJKM > mKML
B. mJKM < mKML
C. mJKM = mKML
D. not enough information

20. Practice #8
Meena and Rita are both flying kites in a field near their houses. Both are using strings that are 10 meters long. Meena’s kite string is at an angle of 75° with the ground. Rita’s kite string is at an angle of 65° with the ground. If they are both standing at the same elevation, which kite is higher in the air?
A. Meena’s kite
B. Rita’s kite

21. Use the Exterior Angle Inequality Theorem to:
Warm Up
Use the Exterior Angle Inequality Theorem to:
List the angles that are greater than m<2
List the angles that are less than m<5
List the angles that are greater than m<8

22. Homework Quiz Write down the work and answer for the following:
1.) pg. 349 #22
2.) Use the figure at the right to determine which angle has the greatest measure.
a) <1, <5, or <6
b) <3, <11, or <12